Question

On a 120km long road, a bus travels the first 30km at a uniform speed of 30km/h. Calculate the speed with which the bus should move for the rest of the journey so as to get an average speed of 60km/h for the entire trip.

Answer 1

Answer:

90 km/h

Explanation:

As per the provided information in the given question, we have :

• On a 120km long road, a bus travels the first 30km at a uniform speed of 30km/h.
• Average speed is 60 km/h.

We are asked to calculate the speed with which the bus should move for the rest of the journey so as to get an average speed of 60km/h for the entire trip.

Let's assume the speed with which the bus should move for the rest of the journey as x.

Now, we need to form a suitable linear equation in order to find the value of x.

We know that,

$\longmapsto\rm {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }$

Here, total distance is 120 km as the bus is travelling on 120 km long road.

Now, we have to find total time :

Firstly we'll find the time taken to cover first 30 km and then we'll find the time taken to cover the rest distance.

Time taken to cover 30 km :

• Distance = 30 km
• Speed = 30 km/h

$\longmapsto\rm {Time= \dfrac{Distance}{Speed} }$

$\longmapsto\rm {t_1= \dfrac{30 \; km }{30 \; kmh^{-1}} }$

$\longmapsto\bf {t_1= 1 \; h }$

Time taken to cover rest of the total distance:

• Distance = (120 - 30) km ⇒ 90 km
• Speed = x

$\longmapsto\rm {Time= \dfrac{Distance}{Speed} }$

$\longmapsto\rm {t_2= \dfrac{90 \; km }{x \; kmh^{-1}} }$

$\longmapsto\bf {t_2= \dfrac{90}{x} \; h }$

Total time :

$\longmapsto\rm {Time_{(Total)} = t_1 + t_2 }$

$\longmapsto\rm {Time_{(Total)} = \Bigg (1 + \dfrac{90}{x} \Bigg ) \; h }$

$\longmapsto\rm {Time_{(Total)} = \Bigg (\dfrac{x + 90}{x} \Bigg ) \; h }$

We know that,

$\longmapsto\rm {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time} }$

Substituting the values.

$\longmapsto\rm {60 = 120 \div \Bigg (\dfrac{x + 90}{x} \Bigg ) }$

$\longmapsto\rm {60 \Bigg (\dfrac{x + 90}{x} \Bigg ) = 120}$

$\longmapsto\rm {\Bigg (\dfrac{x + 90}{x} \Bigg ) = \dfrac{120}{60}}$

$\longmapsto\rm {\dfrac{x + 90}{x} = 2 }$

$\longmapsto\rm {x + 90 = 2x }$

$\longmapsto\rm {90 = 2x - x }$

$\longmapsto\bf {90 = x }$

∴ The bus should move with the speed of 90 km/h for the rest of the journey so as to get an average speed of 60km/h for the entire trip.